By solving the linear inequation it is obtained that [tex]x \leq -3[/tex] or [tex]x \geq 7[/tex].
What is linear inequation?
Expressions with linear inequalities compare any two values using inequality symbols like ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be either numerical, algebraic, or both. Examples of numerical inequalities include 1011 and 20>17, while algebraic inequalities include x>y, y19-x, and x z > 11 (also called literal inequalities). Here is a lesson on linear inequalities for class 11. Inequality in mathematics, linear inequalities, graphing of linear inequalities, as well as detailed examples are all covered in this article.
Here,
The given linear inequation is
[tex]|x - 2| - 3 \geq 2[/tex]
Now,
[tex]|x -2| - 3 \geq 2\\|x - 2| \geq 2+3\\|x-2| \geq 5\\[/tex]
For [tex]x \geq 2\\[/tex]
[tex]x - 2 \geq 5\\x \geq 2 + 5\\x\geq 7[/tex]
For [tex]x < 2[/tex]
[tex]2 - x \geq 5\\x \leq 2 - 5\\x \leq -3[/tex]
So the solution set is [tex]x \leq -3[/tex] or [tex]x \geq 7[/tex]
To learn more about linear inequation, refer to the link:
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graphing on the coordinate plane how does absolute value help you write a number sentence to help you find the distance
Given:
The points 7 and -7.
Required:
We need to find the distance between 7 and -7 by using absolute values.
Explanation:
1)
We need to subtract the given numbers to find the distance.
Subtract 7 from -7 and take absolutely to find the distance.
[tex]Distance=|-7-7|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-7|+|-7|)|[/tex][tex]Distance=|-(7+7)|[/tex][tex]Distance=|-14|[/tex][tex]Distance=14[/tex][tex]We\text{ know that abosulute values of negative number is postive.}[/tex]The absolute value of a number is never negative.
Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
Subtract 5 from -5 and take absolutely to find the distance.
[tex]Distance=|-5-5|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-5|+|-5|)|[/tex][tex]Distance=|-(5+5)|[/tex][tex]Distance=|-10|[/tex][tex]Distance=10[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
3)
Subtract 2 from -2 and take absolutely to find the distance.
[tex]Distance=|-2-2|[/tex][tex]Distance=|-4|[/tex][tex]Distance=4[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
Final answer:
1)
The absolute value of the difference between 7 and -7 is 14.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
The absolute value of the difference between 5 and -5 is 10.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
3)
The absolute value of the difference between 2 and -2 is 4.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
Bх1-7-6-5.-303141516-4Find the distance between A and B.OA. V6 unitsB. 2/3 unitsC. 2V5 unitsD.4 units
With the information in the graph we have to:
[tex]\begin{gathered} AB=\sqrt{4^2+2^2} \\ AB=\sqrt{16+4} \\ AB=\sqrt{20}=\sqrt{2^2\cdot5} \\ AB=2\sqrt{5} \end{gathered}[/tex]therefore the answer is C.
Find the missing length,a, in the right triangle below using the pythagorean theorem.Round to the nearest tenth if necessary.The answer choices are A:28.9 ftB:73.5 ftC:27.1 ftD:4.6 ft
We get that
[tex]a=\sqrt[]{28^2-7^2}=\sqrt[]{784-49}=\sqrt[]{735}\approx27.1[/tex]how manh 1- miligram doses are there in one 2- decagram container?
1 decagram = 10 grams
Also 1000 milligrams = 1 gram
From the information provided, 2 decagrams = 20 grams
If 1000 milligrams = 1 gram, then
1000 x 20 = 20 x 20 grams
20,000 milligrams = 400 grams
Similarly, If 1 decagram = 10 grams, then
0.1 decagram = 1 gram
(that is, divide 1 decagram by 10 and also divide 10 grams by 10)
However, a 2-decagram container can hold 20 grams.
(Remember that 1000 milligrams = 1 gram).
If a 2-decagram container can hold 20 grams, which is equal to 20,000 milligrams, then;
2 decagrams = 20,000 milligrams
Therefore, a 2-decagram container can hold 20,000 1-milligram doses.
11.Graph the function.For the function whose graph is shown below, which is the correct formula for the function?4ns2-4-224Functionss and Functions
To find the formula for the function, we would find the equation of the line in the slope intercept form which is expressed as
y = mx + c
where
m represents slope
c represents y intercept. This is also the point where the line cuts the y axis. Looking at the graph,
c = - 2
We would find the slope by applying the formula,
m = (y2 - y1)/(x2 -x1)
where
y2 and y1 are initial and final values of the y coordinate of two suitable points chosen on the graph
x2 and x1 are initial and final values of the x coordinate of two suitable points chosen on the graph
From the graph,
x1 = - 1, y1 = - 4
x2 = 3, y2 = 4
m = (4 - - 4)/(3 - - 1) = (4 + 4)/(3 + 1) = 8/4
m = 2
Thus, the equation of the graph is
y = 2x - 2
Thus, the correct formula for the function is
y = 2x - 2
PLEASE PLEASE I NEED HELP ANSWERING THIS ITS FOR MY HOMEWORK
In this case the answer is very simple.
We need to write the equation to determine the change in the score.
To find the solution to the exercise we'll have to carry out several steps.
Step 01:
Data
Penalization points = 95
Gained points for each target = 10
Step 02:
Equation
Score change = number of targets* gained points for each target - penalization points
Score change = 4 * 10 - 95
Score change = - 55 points
The answer is:
Sarah's score change = - 55 points
Use the figure below to match each item on the left with the correct side ratio
The right triangle is given with sides a , b and c.
ExplanationTo determine the side ratio of the trigonometric function.
[tex]\begin{gathered} sinA=\frac{a}{c} \\ cosA=\frac{b}{c} \\ tanA=\frac{a}{b} \\ \end{gathered}[/tex][tex]\begin{gathered} sinB=\frac{b}{c} \\ cosB=\frac{a}{c} \\ tanB=\frac{b}{a} \end{gathered}[/tex]AnswerFor sin A , b is correct.
For cos A, d is correct.
For tan A, a is correct.
For sin B, d is correct.
For cos B, b is correct.
For tan B ,c is correct.
Let angle C be congruent to angle C' and POC be congruent to P'O'C'.Let O" be a point on line CO so that CO" is equal to C'O'. Let P" be the point on line CP so that the dilation of P is represented by P".Which statement is true?A. triangle COP is equal to triangle C'O'P'B. line CP is congruent to line CP"C. triangle C'O'P is a glide reflection of triangle COP, whereas triangle CO"P" is congruent to triangle C'O'P'D. triangle CO"P" is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO equals CO/CO
ANSWER
D. Triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO
EXPLANATION
Given:
• ∠C ≅ ∠C'
,• ∠POC ≅ ∠P'O'C'
,• C'O' = CO''
Triangles COP and C'O'P' are similar triangles, by AA postulate.
Since CO'' and C'O' have the same length - they are congruent, then angle CO''P'' is congruent to angle C'O'P', and we can conclude that segments O''P'' and OP are parallel:
Hence, triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO
Below, the two-way table is given for a classof students.FreshmenSophomore Juniors Seniors TotalMale4622Female 3463TotalIf a student is selected at random, find theprobability the student is a male given that it's asophomore.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
We want to calculate the probability the student is a male given that it's a sophomore. Since we already know the student is a sophomore, the possible outcomes are only male sophomores(6) and female sophomores(4) and the favourable outcomes are the male sophomores(6), therefore, this probability is:
[tex]P(Male|Sophomore)=\frac{6}{6+4}=\frac{6}{10}=\frac{60}{100}=60\%[/tex]The probability the student is a male given that it's a sophomore is 60%.
6x = 3/2 what does the x equal to
The equation to be solved is given to be:
[tex]6x=\frac{3}{2}[/tex]To get the value of x in the equation, we just multiply both sides of the equation by 1/6. This is shown below:
[tex]6x\times\frac{1}{6}=\frac{3}{2}\times\frac{1}{6}[/tex]Hence, we have:
[tex]x=\frac{3}{12}[/tex]We can further simplify by dividing the numerator and denominator of the right-hand side by 3. Hence, the answer is:
[tex]x=\frac{1}{4}[/tex]Hi can you help me with this question it is timed i just need an quick answer please and thank you .
ANSWER
EXPLANATION
When triangle DEF is reflected over the y-axis, its vertices are mapped to,
Then, after the translation down 4 units and right 3 units, D' is mapped to S, E' is mapped to R, and F' is mapped to U.
Hence, the congruency statement that describes the two triangles is ΔDEF
A hemisphere bowl of radius 7ft has water in it to a depth of 2 ft. At what angle must it be tipped for the water to begin to flow out?
We have an hemisphere (a shape that is half a sphere) of radius r = 7 ft, that is a bowl filled with water up to a depth of 2 ft.
We have to find at what angle must it be tipped for the water begind to flow. We have to take into account that the level of the water will remain horizontal when we tip the bowl.
This will happen when the water level reaches the edge of the hemisphere.
This can be represented as:
The bowl have to be tipped so the edge descends 2 ft.
We can represent that in mathematical terms as:
Then, we can relate the angle with the depth using a trigonometric ratio:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{\text{depth}}{\text{radius}}=\frac{2}{7} \\ \theta=\arcsin (\frac{2}{7}) \\ \theta\approx16.6\degree \end{gathered}[/tex]Answer: the angle is 16.6°
Angles C and D are acute angles of a right triangle. Given sin D=2/7, which statement is true?
Answer
Option D is correct.
Cos C = (2/7)
Explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
A sketch of this right triangle will be
This sketch allows Sin D = (2/7)
To know the right answer, we need to find the last side of the triangle
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = 2
b = ?
hyp = 7
a² + b² = (hyp)²
2² + b² = 7²
4 + b² = 49
b² = 49 - 4
b² = 45
b = √45
So, we can evaluate each of these
Cos D = (√45)/7
Cos C = (2/7)
Hope this Helps!!!
Answer: cos C = 2/7
Step-by-step explanation: I took the test.
A store has 6 TV Graphic magazines and 8 News time magazines on the counter. If two customers purchased a magazine,find the probability that one each magazine was purchased
SOLUTION:
Case: Probability
Given:
Number of TV Graphic magazines = 6
Number of News time magazines = 8
Total number of magazines on the stand = 14.
*two customers purchased a magazine*
Required: find the probability that one each magazine was purchased
Method:
[tex]\begin{gathered} Pr\left(one\text{ magazine each}\right? \\ =\text{ }\frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ n1=\text{ number of TV graphic magazines} \\ x1=\text{ number of TV graphic magazines selected} \\ n2=\text{ number of News time magazines} \\ x2=\text{ number of News time magazines selected} \\ n=\text{ total number of magazines selected} \\ x=\text{ total number sslected} \end{gathered}[/tex][tex]\begin{gathered} \frac{^{n1}C_{x1}\times^{n2}C_{x2}}{^nC_x} \\ \frac{^6C_1\times^8C_1}{^{^14}C_2} \\ \frac{6\times8}{91} \\ \frac{48}{91} \end{gathered}[/tex]Final answer:
The probability that one each magazine was purchased is 48/91
Write the ratio as a fraction in lowest terms.35 minutes to 5 hours
7 : 60
Explanation:Note that:
1 hour = 60 minutes
5 hours = 5 x 60 minutes
5 hours = 300 minutes
35 minutes : 5 hours = 35 minutes : 300 minutes
35 minutes : 5 hours = 35 : 300
Divide both the numerator and denominator by 5
35 minutes : 5 hours = (35 ÷ 5) : (300 ÷ 5)
35 minutes : 5 hours = 7 : 60
An applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year. Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for Bn that represents the total salary received after n years. Justify your reasoning mathematically.
Offer B canbe represented by an arithmetic sequence because there is a constant difference between the salary of two consecutive years.
The sequence can be written as follow:
Bn = 56,000 + 3,000n
where n is the number of years in the job.
By subtracting B(n+1) - Bn, you obtain:
[tex]\begin{gathered} B_{n+1}-B_n=56,000+3,000(n+1)-56,000-3,000n \\ B_{n+1}-B_n=3,000 \end{gathered}[/tex]As you can notice, the difference of the salaries between two consecutive years is constant, which means that Bn is an arithmetic sequence.
22. Find the 20th term: -30, -22, -14, -6, ....(Hint: Finding the nth term if an Arithmetic Sequence formula: a, = a, + (n − 1)d. )
Arithmetic Sequences
It consists in a series of terms with the condition that each term is calculated as the previous term plus a fixed number called the common difference (d).
The sequence is given as:
-30, -22, -14, -6,...
First, we need to find the common difference by subtracting two consecutive terms:
d = -22 - (-30) = -22 + 30 = 8
We can try another couple of terms:
d = -14 - (-22) = -14 + 22 = 8
If we test all the consecutive terms, we'll find the same value of d.
Now to use the formula:
an = a1 + (n - 1) * d
We need to find a1, the first term of the sequence. The value of a1 is -30.
Now we are ready to find the 20th term of the sequence (n=20) by substituting the values in the formula:
a20 = -30 + (20 - 1) * 8
Calculating:
a20 = -30 + 19 * 8 = -30 + 152 = 122
Thus the 20th term is 122
4. The perimeter of a rectangular garden is 36 feet. The length of the garden is 6 less than twicethe width. Find the length and width of the garden.Variable:Equation:Variable:Equation:LengthWidth
From the question, we've been given the perimeter of the rectangular garden to be 36ft and we're told that the length is 6 less than twice the width of the garden
I need help on solving this Did I get the right answer ? And do the table right ?
quadratic function with x intercepts -1 and 1
quadratic function with x intercepts -1 and 1:
[tex]f(x)=(x+1)(x-1)=x^2-x+x+1=x^2+1[/tex]can you please help me
we have the equation
y=-4x+4
this is the equation of the line in slope intercept form
where
the slope is m=-4 ----> is a negative slope
the y-intercept is b=4
that means
the y-intercept is the point (0,4)
Find out the x-intercept
For y=0
0=-4x+4
4x=4
x=1
x intercept is (1,0)
therefore
the answer is
a line that slopes down
watch your P's and Q's texas instruments incorporated
Start by graphing your function in the calculator or systme you are using to graph.
we can get closer to the zeros of the functions.
The zeros of a function are the points the function cross over the x-axis, menaing that y is always 0.
According to the graph the functions has 2 zeros.
The approximate zeros will be (-9,0) and (0,0) since they are the closer to the actual point crossing th x.-axis.
I need to graph thid inequality, while showing work. I get some right and others wrong.
Y < 2x^2 - 1
Then first graph equation parabolic
2x^2 -1,
Then draw green lines , below 2x^2 -1
Debra started washing at 8:33 AM and finished at 9:22 AM.How long did it take her? Give your answer in minutes.
According to the given data we have the following:
Debra started washing at 8:33 AM
finished at 9:22 AM
One easy way to find out the amount of time it took to her washing her clothes would be the following:
Debra started washing at 8:33 AM, so from 8:33 am to 9 o clock 27 minutes passed.
So, if she finished at 9:22 AM, that means that we would have to add to the 27 minutes another 22 minutes, so 27+22=49 minutes.
Therefore, it took to her 49 minutes to wash her clothes.
use a model to solve2/3×6
Here, we want to use a model to solve the multiplication
We have this as follows;
Mathematically;
[tex]\frac{2}{3}\times6\text{ = 4}[/tex]Solve the system by substitution.4x – 2y = -4y = 3x
We start by substituting the value of 3x for y in the first equation
We have this as;
[tex]\begin{gathered} 4x-2(3x)\text{ = -4} \\ 4x\text{ - 6x = -4} \\ -2x=\text{ -4} \\ x\text{ = }\frac{-4}{-2} \\ x\text{ =2} \\ \text{From i}i\colon\text{ y = 3x ; y = 3(2) ; y = 6} \end{gathered}[/tex]< Previous1Next >Factoring Polynomials: Mastery Test1Select the correct answer.What is the completely factored form of this polynomial?x3 + 3x2 - 6x-18A. (x-2)(x - 3)(x + 3)OB. (x2 - 6/x+3)C. (x2 + 3)(x-6)OD. (x+6)(x - 1)(x + 3)ResetNext
Solution
[tex]x^3+3x^2-6x-18[/tex]We can do the following:
[tex]x^2(x+3)-6(x+3)=(x+3)(x^2-6)[/tex]Then the correct answer would be:
[tex]B\mathrm{}(x^2-6)(x+3)[/tex]For the second case we have the following:
[tex]9x^2-64y^2[/tex]We can do this:
[tex](3x-8y)(3x+8y)[/tex]I need to know what 152x4241 is
Multiplying:
[tex]152\cdot4241=644632[/tex]Answer: 644632
The junior class is selling fruit bars to raise money. They purchased 1250 fruit bars and paid a delivery fee of $25. The total cost, including the delivery fee, was $800. What was the cost of each bar?
Number of fruit bars purchased = 1250.
Delivery fee = $25
Total cost including the delivery fee = $800.
Therefore, the cost without delivery fee = 800-25 = $775.
Therefore, the cost of fruit bars purchased = $ 775.
So, the cost of 1 fruit bar, is,
[tex]\frac{775}{1250}=0.62[/tex]Therefore, the cost of 1 fruit bar is $ 0.62.
14. Imagine a particle starting at (1,0) and making one counterclockwise revolution on the unitcircle. Let t be the angle in standard position that corresponds to the particle's position. At howmany points along the path of the particle are the x and y coordinates equal?
Let's make a graph to better understand the question:
a.) A particle starting at (1,0) and making one counterclockwise revolution on the unit
circle.
In the given description, we can assume that the center of the circle when the particle makes a revolution is at the origin (0,0). Thus, the equation of the circle that the particle will make is:
[tex](x-h)^2+(y-k)^2\text{ = }r^2[/tex]At (h,k) = (0,0) and r = distance between (0,0) to (1,0).
We get,
[tex](x-0)^2+(y-k)^2=(\sqrt[]{(1-0)^2+(0-0)^2})^2[/tex][tex]x^2+y^2\text{ = }1[/tex]Plotting the graph,
In conclusion, there will be two points along the path of the particle that the x and y coordinate equal.
At, x = y, let's substitute this to the formula of the graph of the circle to get the coordinates.
[tex]x^2+y^2\text{ = }1[/tex][tex]x^2+x^2\text{ = }1[/tex][tex]2x^2\text{ = 1 }\rightarrow\text{ }\frac{2x^2}{2}=\text{ }\frac{1}{2}[/tex][tex]x\text{ = }\sqrt[]{\frac{1}{2}}[/tex][tex]x\text{ = y = }\pm\frac{1}{\sqrt[]{2}}[/tex]Therefore, the two points where the x and y will be equal is at:
[tex]\text{ x = y = +}\frac{1}{\sqrt{2}}\text{ and }-\frac{1}{\sqrt[]{2}}[/tex]